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An Introduction to Groups
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algebra arbitrary assume basis vectors bilinear form called canonical form Cauchy sequence characteristic polynomial column consider converges corollary to Theorem define definition denote det(xl diagonal matrix diagonalizable direct sum eigenvalues eigenvectors element elementary divisors entries equation equivalent Example Exercise exists fact factors field finite number function given hence Hermitian Hilbert space implies inner product space integer integral domain inverse isomorphism linear operator linear transformation linearly independent mapping matrix representation metric space minimal polynomial Mn(C Mn(J monic multiplication mv(x n x n nonsingular nonzero norm notation Note orthogonal orthonormal basis orthonormal set permutation prime Proof Let proof of Theorem prove real numbers result ring row-echelon form scalar Section spanned subset suppose symmetric T-invariant subspace tensor unique unitary unitary matrix words write zero